The two posted IR signals (written in Pronto Hex notation) are identical. After the first 4 numbers, the remaining numbers are just pairs of on and off durations expressed in hedadecimal notation (base 16) in units of the modulation period of the IR light. The IR frequency here is 38KHz, so the endng 303 versus 304 "difference" is really 26 microseconds on a duration of 20072 microseconds. Completely insignificant.
Air conditioners typically are controlled differently from AV components. In AV equipment, pressing e.g. Volume Up on the remote will always send the same command to the AV--increment the volume. The AV keeps track of the actual volume level. In most ACs, the remote remembers e.g. the temperature and pressing Temp Up sends a different signal each time. That is, it actually sends the requested temperature and not a increment temperature signal. Your signals have 64 bits of information, and probably the complete state of the AC is being sent on each press of any button.
Check whether this is true by setting the AC to the minimum temperature and record each IR signal as you increase temperature. I like to use the Import function of IR Scope
to get a decode of the signal. That's a lot easier to read than the Pronto Hex notation.
If you think you still want to use your GC hardware to control the AC, we'll need to figure out the format of the commands. That can be done by systematically recording the IR signals for each possible state associated with a button, keeping track of which signal corresponds to any state. Then we can parse out which bits control each function.